But Bayliss said the door was still open for the hard-hitting batsman, who has played 70 ODIs and 60 T20Is.

"Alex still has an international future," Bayliss told Sky Sports. "I have spoken to him and given him that message.

"It's certainly not the end of him. He's a very important player and there is no reason why he can't come back."

He added: "I think we've come to the right decision. Being respected off the field as well as on it is very important."

The England coach said the selectors would have to make a "very difficult decision" following an impressive show from Jofra Archer, who made his debut against Ireland last week.

Speaking about the Barbados-born all-rounder, Bayliss said: "He's fitted into the group extremely well. He's a fairly quiet sort of a guy. He looked very nervous in that first game in Ireland as anyone making their debuts usually are.

"I thought he bowled some good spells, or one or two spells in Ireland without too much luck and I thought he bowled pretty well in the T20 match a couple of days ago.

"It's all looking good. It's going to be a very difficult decision for the selectors, whichever way we go."